A292408
Number of 3-regular maps with 2n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
1, 5, 46, 669, 11096, 196888, 3596104, 66867564, 1258801076, 23925376862, 458284630844, 8835496339452, 171286387714900, 3336406717216564, 65257828878990784, 1281049596756607960, 25228921286295314736, 498287389997552607290, 9866927329534881618772, 195837489338961245840240
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225[math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
- Riccardo Murri, Fatgraph algorithms and the homology of the Kontsevich complex, arXiv preprint arXiv:1202.1820, 2012.
3-regular maps on the sphere:
A112948.
A292971
Number of 4-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
1, 4, 23, 185, 1647, 16455, 169734, 1805028, 19472757, 212603589, 2341275180, 25969695728, 289782412836, 3250137255678
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A292974
Number of 6-regular maps with n vertices on the torus, up to orientation-preserving isomorphisms.
Original entry on oeis.org
3, 81, 3313, 171282, 9444158, 541659909, 31819176850, 1902508129720, 115307287484560, 7064528615347192, 436658221692698200, 27188662712300575980, 1703444238720524912060
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part I: Enumeration of Rooted and Sensed Maps, arXiv preprint arXiv:1709.03225 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part I: Rooted maps on the torus, the projective plane and the Klein bottle. Sensed maps on the torus, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 584-599.
A301425
Number of plane 5-regular simple connected graphs with 2n vertices.
Original entry on oeis.org
1, 0, 1, 1, 6, 14, 98, 529, 4035, 31009, 252386, 2073769, 17277113
Offset: 6
There is only a(6) = 1 planar 5-regular simple connected graph with 2n = 12 vertices, which is the icosahedral graph, cf. MathWorld link. If we label the vertices 1, ..., 9, A, B, C, they are connected as follows: 1 -> {2 3 4 5 6}, 2 -> {1 6 7 8 3}, 3 -> {1 2 8 9 4}, 4 -> {1 3 9 A 5}, 5 -> {1 4 A B 6}, 6 -> {1 5 B 7 2 }, 7 -> {2 6 B C 8}, 8 -> {2 7 C 9 3}, 9 -> {3 8 C A 4}, A -> {4 9 C B 5}, B -> {5 A C 7 6}, C -> {7 B A 9 8}.
For other numbers of vertices, the number of plane 5-regular simple connected graphs is as follows:
14 vertices: 0 graphs,
16 vertices: 1 graph,
18 vertices: 1 graph,
20 vertices: 6 graphs,
22 vertices: 14 graphs,
24 vertices: 98 graphs,
26 vertices: 529 graphs,
28 vertices: 4035 graphs,
30 vertices: 31009 graphs,
32 vertices: 252386 graphs,
34 vertices: 2073769 graphs,
36 vertices: 17277113 graphs. (From the McKay web page.)
Showing 1-4 of 4 results.
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